Dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts

Dynamic behavior of mixing fronts plays a crucial role in multifluid turbulent mixing. In this paper, we derive an analytic solution for the dynamic evolution of mixing fronts driven by constant acceleration Rayleigh-Taylor (RT) and impulsive acceleration Richtmyer-Meshkov instabilities, from a simple physics model expressed as a pair of ordinary differential equations. An approximate closed form asymptotic evaluation of the RT solution is obtained, through terms of order O(1), as t--> infinity. This three term expansion, including lower order terms, is used to interpret experimental and simulation data. Our solutions improve on previous analyses in their agreement with experimental data, in that we can fit both the slope and the intercept of the Z(b) vs Agt(2) experimental plots by adjusting parameters in our model. Since the experimental data are close to self-similar, the improvement due to the lower order contributions in the asymptotic expansion is modest. We also apply this analysis to simulation data, for which preasymptotic data exist. We reexamine previous simulation data and determine an improved growth rate alpha(b)=0.0625. The present paper provides concepts and tools to explore the preasymptotic aspects of these data.